偏序集上的弱滤子弱极大理想

摘要

In this paper,the concept of weak maximal ideals relative to weak filters on posets is introduced and examined. The existence of maximal ideals relative to filters is proved,and its some properties are stud-ied.In addition,in the posets with discending chain condition of weak ideals,every weak ideal of posets can be decomposed as intersection of some weak maximal ideals relative to weak filters.%文章在偏序集上引入偏序集上弱滤子弱极大理想，证明其存在性定理，并研究它的一些性质，得到弱理想在满足弱理想降链条件的偏序集上的一个分解定理。